LINEAR AND NONLINEAR-THEORY OF EIGENFUNCTION SCARS

The theory of scarring of eigenfunctions of classically chaotic system s by short periodic orbits is extended in several ways. The influence of short-time linear recurrences on correlations and fluctuations at l ong times is emphasized. We include the contribution to scarring of no nlinear recurrences associated with homoclinic orbits and treat the di fferent scenarios of random and nonrandom long-time recurrences. The i mportance of the local classical structure around the periodic orbit i s emphasized. and it is shown for an optimal choice of test basis in p hase space that scars must persist in the semiclassical limit. Thr cru cial role of symmetry is also discussed which, together with the nonli near recurrences gives a much improved account of the actual strength of scars for given classical orbits and in individual wave-functions. Quantitative measures of scarring are provided and comparisons are mad e with numerical data. (C) 1998 Academic Press.